math 71 10.1 – distance and midpoint formulas; circles 1
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Math 71
10.1 – Distance and Midpoint Formulas; Circles
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The Distance Formula
Can use Pythagorean Theorem to get the distance formula:
Suppose you’re looking for the distance from point at to point at .
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Ex 1.Find the distance between and .
The Distance Formula
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The Midpoint Formula
Midpoint formula:
Ex 2.Find the midpoint of the segment with endpoints and .
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The Midpoint Formula
Midpoint formula:
Ex 2.Find the midpoint of the segment with endpoints and .
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The Midpoint Formula
Midpoint formula:
Ex 2.Find the midpoint of the segment with endpoints and .
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The Midpoint Formula
Midpoint formula:
Ex 2.Find the midpoint of the segment with endpoints and .
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A circle is the set of all points a given distance (__________) from a given point (__________).
Circles
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A circle is the set of all points a given distance (__________) from a given point (__________).
Circles
radius
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A circle is the set of all points a given distance (__________) from a given point (__________).
Circles
radius center
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Squaring both sides, we get the standard form of the equation of a circle with center and radius :
Circles
What’s the distance from the center to any point on the circle ?
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Squaring both sides, we get the standard form of the equation of a circle with center and radius :
Circles
What’s the distance from the center to any point on the circle ?
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Squaring both sides, we get the standard form of the equation of a circle with center and radius :
Circles
What’s the distance from the center to any point on the circle ?
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Ex 3.Find the standard form of the equation for a circle with center and radius , and graph it.
Circles
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Ex 3.Find the standard form of the equation for a circle with center and radius , and graph it.
Circles
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Ex 3.Find the standard form of the equation for a circle with center and radius , and graph it.
Circles
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Ex 3.Find the standard form of the equation for a circle with center and radius , and graph it.
Circles
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Ex 4.Find the center and radius of the circle whose equation is , and graph it.
Circles
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Ex 4.Find the center and radius of the circle whose equation is , and graph it.
Circles
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Ex 4.Find the center and radius of the circle whose equation is , and graph it.
Circles
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Ex 4.Find the center and radius of the circle whose equation is , and graph it.
Circles
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The general form of the equation of a circle is
We can convert from general form to standard form by ________________________.
Ex 5.Write in standard form:
Circles
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The general form of the equation of a circle is
We can convert from general form to standard form by ________________________.
Ex 5.Write in standard form:
Circles
completing the square
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The general form of the equation of a circle is
We can convert from general form to standard form by ________________________.
Ex 5.Write in standard form:
Circles
completing the square